a) 8x3 - 64 = (2x)3 - 43
= (2x - 4)\([\)(2x)2 + 2x.4 + 42\(]\)
= (2x - 4)(4x2 + 8x + 16)
b) 1 + 8x6y3
= 13 + (2x2y)3
= (1 + 2x2y)[(2x2y)2 - 2x2y.1 + 12]
= (1 + 2x2y)(4x4y2 - 2x2y + 1)
c) 27x3 + \(\frac{y^3}{8}\)
= (3x)3 + \(\left(\frac{y}{2}\right)^3\)
= \(\left(3x+\frac{y}{2}\right)\left[\left(3x\right)^2-3x.\frac{y}{2}+\left(\frac{y}{2}\right)^2\right]\)
= \(\left(3x-\frac{y}{2}\right)\left(9x^2-\frac{3xy}{2}+\frac{y^2}{4}\right)\)
d) 125x3 + 27y3
= (5x)3 + (3y)3
= (5x + 3y)[(5x)2 - 5x.3y + (3y)2]
= (5x + 3y)(25x2 - 15xy + 9y2)
a) \(8x^3-64\)
\(=\left(2x\right)^3-4^3\)
\(=\left(2x-4\right)\left[\left(2x\right)^2+2x.4+4^2\right]\)
\(=\left(2x-4\right)\left(4x^2+8x+16\right)\)
d) \(125x^3+27y^3\)
\(=\left(5x\right)^3+\left(3y\right)^3\)
\(=\left(5x+3y\right)\left[\left(5x\right)^2-5x.3y+\left(3y\right)^2\right]\)
\(=\left(5x+3y\right)\left(25x^2-15xy+9y^2\right)\)
